Sentiment lexicon is an important tool for identifying the sentiment polarity of words and texts. How to automatically construct sentiment lexicons has become a research topic in the field of sentiment analysis and opinion mining. Recently there were some attempts to employ representation learning algorithms to construct a sentiment lexicon with sentiment-aware word embedding. However, these methods were normally trained under document-level sentiment supervision. In this paper, we develop a neural architecture to train a sentiment-aware word embedding by integrating the sentiment supervision at both document and word levels, to enhance the quality of word embedding as well as the sentiment lexicon. Experiments on the SemEval 2013-2016 datasets indicate that the sentiment lexicon generated by our approach achieves the state-of-the-art performance in both supervised and unsupervised sentiment classification, in comparison with several strong sentiment lexicon construction methods.